Extending a Lego package. An extension of the coin package for - PowerPoint PPT Presentation

Extending a Lego package. An extension of the coin package for comparing interventions assigned by dynamic allocation Johannes H¨ using Coordination Center for Clinical Trials, Heidelberg Medical School 2008-08-13

Outline 1 Sequential Balancing Designs 2 Re-randomization extension 3 Building blocks of dynamic allocation 4 Result 5 Discussion

History on Randomization • Randomization initially had to find its place among systematic designs. • Paul Martini, a forerunner of clinical trials in Germany, used alternation in an early form of cross-over trials (Shelley & Baur, 1999). • In clinical trials, randomization had found its place at the top. • Nevertheless, random allocation sometimes leads to unbalanced distribution between treatment arms.

Some Discussion of Randomized Designs Those who habitually use random assignments may have thought that the issue was finally settled in favour of randomization, but the recent recrudescence of the dispute . . . make[s] it clear that there is still a considerable body of opinion which favour such arrangements. Yates (1938) But in either case, as soon as the experiment is designed, [experimental conditions] are definitely known . . . , and not random any longer. Jeffreys (1938)

New Discussion, new Variants • biased coin (not coin !) Efron (1971) • minimization Taves (1974) • (optimal stratification) Sedransk (1974) • adaptive allocation Pocock & Simon (1975) • dynamic balanced randomization Signorini (1993) • generalization to continuous covariates incorporating Kullback-Leibler loss

New Discussion, new Variants • biased coin (not coin !) Efron (1971) • minimization Taves (1974) • (optimal stratification) Sedransk (1974) • adaptive allocation Pocock & Simon (1975) • dynamic balanced randomization Signorini (1993) • generalization to continuous covariates incorporating Kullback-Leibler loss Idea: achieve balance

Reservations in Regulatory Bodies Dynamic allocation is strongly discouraged. However, if it is used, then it is imperative that all factors used in the allocation scheme be included as covariates in the analysis. Even with this requirement, it remains controversial whether the analysis adequately reflect the randomisation scheme. EMEA (2003)

Outline 1 Sequential Balancing Designs 2 Re-randomization extension 3 Building blocks of dynamic allocation 4 Result 5 Discussion

Reflect the Randomization Scheme Can be accomplished by re-randomization methods (Simon 1979) . Idea: Repeat the same algorithm over original sequence of patients. Obtain null distribution, define critical region and determine if test statistic is in it. This idea is very similar to the permutation test.

Freeloading on an existing interface The package coin offers a common interface to permutation test methods. Choice between: 1 exact, 2 asymptotic (Strasser and Weber 1999) , 3 approximate (Monte Carlo) methods. For re-randomization methods, Monte Carlo only choice.

Classes in the coin package QuadTypeIndependenceTestStatistic ScalarIndependenceTestConfint ScalarIndependenceTest covarianceplus df confint conf.level nullvalue IndependenceTestProblem matrix numeric function numeric numeric xtrans ytrans xtrafo ytrafo IndependenceTest IndependenceProblem MaxTypeIndependenceTest matrix matrix function function distribution statistic method x y weights block SymmetryProblem NullDistribution IndependenceTestStatistic character data.frame data.frame numeric factor QuadTypeIndependenceTest IndependenceTestStatistic IndependenceLinearStatistic MaxTypeIndependenceTestStatistic estimates teststatistic standardizedlinearstatistic linearstatistic expectation covariance alternative character VarCovar list numeric numeric numeric numeric VarCovar ScalarIndependenceTestStatistic Variance alternative variance numeric character CovarianceMatrix ApproxNullDistribution covariance NullDistribution PValue matrix q d support parameters pvalue p name ExactNullDistribution function function function list function function character AsymptNullDistribution Want to mess with the approximate null distribution. ApproxNullDistribution is a method on ScalarIndependenceTestStatistic . Need algorithm for reallocation and possibly a shuffling algorithm.

Classes in the coin package QuadTypeIndependenceTestStatistic covarianceplus df matrix numeric IndependenceTest t distribution statistic method NullDistribution IndependenceTestStatistic character st IndependenceTestStatistic Independenc MaxTypeIndependenceTestStatistic estimates teststatistic standardizedlinearstatistic linearstatistic ex alternative character list numeric numeric numeric n ScalarIndependenceTestStatistic alternative character ApproxNullDistribution NullDistribution P q d support parameters pvalue ExactNullDistribution function function function list function fun AsymptNullDistribution

ScalarIndependenceTestConfint ScalarIndependenceTest Messing with the coin package confint conf.level nullvalue function numeric numeric MaxTypeIndependenceTest IndependenceTest QuadTypeIndependenceTest distribution statistic metho NullDistribution IndependenceTestStatistic charact QuadTypeIndependenceAllocTestStatistic QuadTypeIndependenceTestStatistic algorithm shuffle covarianceplus df function function matrix numeric ScalarIndependenceAllocTestStatistic ScalarIndependenceTestStatistic algorithm function alternative shuffle function character MaxTypeIndependenceAllocTestStatistic MaxTypeIndependenceTestStatistic algorithm shuffle alternative character function function ApproxNullDistribution ExactNullDistribution AsymptNullDistribution

Messing with the coin package IndependenceAllocProblem algorithm shuffle function function ceAllocTestProblem IndependenceTestProblem IndependenceProblem xtrans ytrans xtrafo ytrafo x y weights block enceLinearStatistic matrix matrix function function data.frame data.frame numeric factor expectation covariance SymmetryProblem numeric VarCovar VarCovar Variance variance numeric CovarianceMatrix covariance PValue matrix p name function character

Messing with the coin package IndependenceAllocProblem algorithm shuffle function function eAllocLinearStatistic IndependenceAllocTestProblem IndependenceTestProblem IndependenceP xtrans ytrans xtrafo ytrafo x y enceTestStatistic IndependenceLinearStatistic matrix matrix function function data.frame data.frame c standardizedlinearstatistic linearstatistic expectation covariance SymmetryProblem numeric numeric numeric VarCovar VarCovar Variance variance numeric CovarianceMatrix covariance Distribution PValue matrix support parameters pvalue p name n function list function function character

Messing with the coin package estStatistic IndependenceA algorithm function stStatistic IndependenceAllocLinearStatistic IndependenceAllocTestProblem Independence xtrans ytrans TestStatistic IndependenceTestStatistic IndependenceLinearStatistic matrix matrix f df estimates teststatistic standardizedlinearstatistic linearstatistic expectation covariance Symmetry numeric list numeric numeric numeric numeric VarCovar TestStatistic VarC character est Varia ic method variance estStatistic character Covarianc ution covar NullDistribution PValue mat q d support parameters pvalue p name ibution function function function list function function character bution

Messing with the coin package ScalarIndependenceTestStatistic estStatistic alternative character IndependenceAllocTestStatistic IndependenceAllocLinearStatistic Independen estStatistic QuadTypeIndependenceTestStatistic IndependenceTestStatistic Independ estStatistic covarianceplus df estimates teststatistic standardizedlinearstatistic linearstatistic matrix numeric list numeric numeric numeric ceTest MaxTypeIndependenceTestStatistic alternative character Test IndependenceTest distribution statistic method NullDistribution IndependenceTestStatistic character ceTest ExactNullDistribution NullDistribution q d support parameters pvalue AsymptNullDistribution function function function list function ApproxNullDistribution

Messing with the coin package ScalarIndependenceTestStatistic ScalarIndependenceAllocTestStatistic alternative character IndependenceAllocTestStatistic Independence QuadIndependenceAllocTestStatistic QuadTypeIndependenceTestStatistic Independ MaxIndependenceAllocTestStatistic covarianceplus df estimates teststatisti matrix numeric list numeric QuadTypeIndependenceTest MaxTypeIndependenceTestStatistic alternative character ndenceTestConfint ScalarIndependenceTest IndependenceTest conf.level nullvalue distribution statistic method numeric numeric NullDistribution IndependenceTestStatistic character MaxTypeIndependenceTest ExactNullDistribution Null q d AsymptNullDistribution function functio ApproxNullDistribution

Outline 1 Sequential Balancing Designs 2 Re-randomization extension 3 Building blocks of dynamic allocation 4 Result 5 Discussion

More Lego bricks: goodarms goodarms • Takes the data frame of predictors and allocations up to now • Returns treatment arms with the least loss lossfun() goodarms() arms with smallest loss